How do you find the GCF of #64x^8y^3#, #40x^6y^8#?

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Answer 1 · 2018-03-20T05:19:25

GCF #= 8x^6y^3#

Given: Find GCF of #64x^8y^3 " and " 40x^6y^8#

GCF is the greatest common factor.

#64x^8y^3 = color(red)(2*2*2)*2*2*2*color(red)(x*x*x*x*x*x)*x*x*color(red)(y*y*y)#

#40x^6y^8 = color(red)(2*2*2)*5*color(red)(x*x*x*x*x*x)*color(red)(y*y*y)*y*y*y*y*y#

The GCF = #2*2*2*x*x*x*x*x*x*y*y*y = 8x^6y^3#

A simpler way to find the GCF use the exponent rule: #x^mx^n = x^(m+n)#

#x^8 = x^6x^2; " "y^8 = y^3y^5#

So,
#64x^8y^3 = color(red)(8)*8color(red)(x^6)x^2color(red)(y^3)#

#40x^6y^8 = color(red)(8)*5color(red)(x^6)color(red)(y^3)y^5#

GCF = #8x^6y^3#